Skip to main content
Log in

Equilibrium Points in the Restricted Four-Body Problem with Radiation Pressure

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

This paper studies numerically the photogravitational version of the restricted four-body problem, where an infinitesimal particle is moving under the gravitational attraction and radiation pressure of three bodies much bigger than the particle, the primaries. The fourth body does not affect the motion of the three bodies. These bodies are always at the vertices of an equilateral triangle (Lagrange configuration). We consider all the primary bodies (m 1, m 2, m 3) as radiation sources with radiation factors of the two bodies (m 2 and m 3) equal. In this paper we suppose the masses of the three primary bodies are equal. It is found that the involved parameters influenced the positions of the equilibrium points. The linear stability of the relative equilibrium solutions is also studied and all these points are unstable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baltagiannis, A.N., Papadakis, K.E.: Equilibrium points and their stability in the restricted four-body problem. Int. J. Birfucat Chaos. Appl. Sci. Eng. 21, 2179–2193 (2011a)

  2. Kalvouridis T.J.: The effect of radiation pressure on the particle dynamics in ring type N-body configurations. Earth Moon Planets 87, 87–102 (2001)

    Article  ADS  Google Scholar 

  3. Kalvouridis T.J, Arribas M., Elipe A.: Dynamical properties of the restricted four-body problem with radiation pressure. Mech. Res. Commun. 33, 811–817 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kumar V., Choudhry R.K.: Linear stability and the resonance cases for the triangular libration points for the doubly photogravitational elliptic restricted problem of three bodies. Celest. Mech. Dyn. Astron. 46, 59–77 (1989)

    Article  MATH  ADS  Google Scholar 

  5. Kunitsyn A.L., Polyakhova E.N.: The restricted photogravitational three-body problem. Astron. Astrophys. Trans. 6, 283–293 (1995)

    Article  ADS  Google Scholar 

  6. Luk’yanov L.G.: Stability of Coplanar libration points in the restricted photogravitational three-body problem. Sov. Astron. 31, 677–681 (1987)

    MATH  MathSciNet  ADS  Google Scholar 

  7. Markellos V.V., Perdios E., Papadakis K.E.: The stability of inner collinear equilibrium points in the photogravitational elliptic restricted problem. Astrophys. Space Sci. 199, 139–146 (1993)

    Article  MATH  ADS  Google Scholar 

  8. Markellos V.V., Roy A.E., Velgakis M.J., Kanavos S.S.: A photogravitational Hill problem and radiation effects on Hill stability of orbits. Astrophys. Space Sci. 271, 293–301 (2000)

    Article  MATH  ADS  Google Scholar 

  9. Papadouris J.P., Papadakis K.E.: Equilibrium points in the photogravitational restricted four-body problem. Astrophys. Space Sci. 344, 21–38 (2013)

    Article  MATH  ADS  Google Scholar 

  10. Radzievskii V.V.: The restricted problem of three-bodies taking account of light pressure. Astron. J. 27, 250–256 (1950)

    MathSciNet  Google Scholar 

  11. Radzievskii, V.V.: Zadacha dvuh gravitiruyoushih I izluchayoushih tel. Astron. J. 28, 363–372 (1951)

  12. Radzievskii V.V.: The space photogravitational restricted three-body. Astron. J. 30, 265 (1953)

    MathSciNet  Google Scholar 

  13. Ragos O., Zafiropoulos F.A.: A numerical study of the influence of the Poynting–Robertson effect on the equilibrium points of the photo-gravitational restricted three-body problem. Astron. Astrophys. 300, 568 (1995)

    ADS  Google Scholar 

  14. Simmons J., McDonald A., Brown J.: The restricted 3-body problem with radiation pressure. Celest. Mech. 35, 145–187 (1985)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. Singh J.: Combined effects of oblateness and radiation on the nonlinear stability of L4 in the restricted three-body problem. Astron. J. 137, 3286 (2009)

    Article  ADS  Google Scholar 

  16. Singh J., Leke O.: Stability of the photogravitational restricted three-body with variable masses. Astrophys. Space Sci. 326, 305 (2010)

    Article  MATH  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aguda Ekele Vincent.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, J., Vincent, A.E. Equilibrium Points in the Restricted Four-Body Problem with Radiation Pressure. Few-Body Syst 57, 83–91 (2016). https://doi.org/10.1007/s00601-015-1030-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00601-015-1030-8

Keywords

Navigation